The electrical systems on these units, especially if this is a mid 90s model, which it sounds like it might be based on your description are very very simple. There isn't but a handful of wires. If it isn't something obvious like a chewed through piece of wire, start using a voltmeter for continuity. Honestly, I would probably go straight to the starter solenoid. In a relentless effort to punish China, I often buy stuff like this on Amazon for seven dollars purely for testing purposes. If it works, you can buy one of the high dollar ones from John Deere and then send the one from Amazon back. Truth be told, John Deere probably buys it from China anyway. That's where I would start.

If you hit the start key, and nothing happens, I start looking at solenoids, if you hit the start key and it clicks, I looked directly at the starter. These John Deere units for whatever reason have starters that are very fickle. I have several gators and most of them have a piece of rebar in the bed specifically for tapping the starter when they start giving me trouble lol

Test voltage at the starter. No click? Also check your battery connections. Had a starting issue and it was a bad connection.

Is it in neutral?